This proof fails to validate that the number placed in d[i,j] is in
fact minimal; this is more difficult to show, and involves an argument
by contradiction in which we assume d[i,j] is smaller than the minimum
of the three, and use this to show one of the three is not minimal.

So how can I show that d[i,j] is actually minimal? (informal proof is ok)

1 Answer
1

There is an optimal edit sequence in which the edit operations occur in order from left to right. There are only three options for the last edit operation: insert the last character of the target string, delete the last character of the source string, or replace the last character. Everything before the last edit operation must be optimal.